A double-distribution-function lattice Boltzmann model for high-speed compressible viscous flows

2018 ◽  
Vol 166 ◽  
pp. 24-31 ◽  
Author(s):  
Ruo-Fan Qiu ◽  
Cheng-Xiang Zhu ◽  
Rong-Qian Chen ◽  
Jian-Feng Zhu ◽  
Yan-Cheng You
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
High Speed ◽  
Viscous Flows ◽  
Lattice Boltzmann Model ◽  
Function Lattice ◽  
Compressible Viscous Flows ◽  
Boltzmann Model

A Hermite-based lattice Boltzmann model with artificial viscosity for compressible viscous flows

2018 ◽  
Vol 32 (13) ◽  
pp. 1850157 ◽  
Author(s):  
Ruofan Qiu ◽  
Rongqian Chen ◽  
Chenxiang Zhu ◽  
Yancheng You
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
Viscous Flows ◽  
Artificial Viscosity ◽  
Lattice Boltzmann Model ◽  
Hermite Expansion ◽  
Discrete Velocity ◽  
Velocity Models ◽  
Compressible Viscous Flows ◽  
Boltzmann Model

A lattice Boltzmann model on Hermite basis for compressible viscous flows is presented in this paper. The model is developed in the framework of double-distribution-function approach, which has adjustable specific-heat ratio and Prandtl number. It contains a density distribution function for the flow field and a total energy distribution function for the temperature field. The equilibrium distribution function is determined by Hermite expansion, and the D3Q27 and D3Q39 three-dimensional (3D) discrete velocity models are used, in which the discrete velocity model can be replaced easily. Moreover, an artificial viscosity is introduced to enhance the model for capturing shock waves. The model is tested through several cases of compressible flows, including 3D supersonic viscous flows with boundary layer. The effect of artificial viscosity is estimated. Besides, D3Q27 and D3Q39 models are further compared in the present platform.

AN IMPROVED THERMAL LATTICE BOLTZMANN MODEL FOR FLOWS WITHOUT VISCOUS HEAT DISSIPATION AND COMPRESSION WORK

2008 ◽  
Vol 19 (01) ◽  
pp. 125-150 ◽  
Author(s):  
Q. LI ◽  
Y. L. HE ◽  
Y. WANG ◽  
G. H. TANG
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
Heat Dissipation ◽  
Lattice Boltzmann Model ◽  
Two Dimensional ◽  
Bgk Model ◽  
Function Lattice ◽  
Viscous Heat ◽  
Boltzmann Model ◽  
Benchmark Solutions

An improved lattice Boltzmann model is proposed for thermal flows in which the viscous heat dissipation and compression work by the pressure can be neglected. In the improved model, the whole complicated gradient term in the internal energy density distribution function model is correctly discarded by modifying the velocity moments' condition. The corresponding macroscopic energy equation is exactly derived through Chapman–Enskog expansion. In particular, based on the improved thermal model, a double-distribution-function lattice BGK model is developed for two-dimensional Boussinesq flow, which is a typical flow with negligible viscous heat dissipation and compression work. A two-dimensional plane flow and the natural convection of air in a square cavity with various Rayleigh numbers are simulated by using the double-distribution-function lattice BGK model. It is found that there is excellent agreement between the present results with the analytical or benchmark solutions.

Incompressible lattice Boltzmann model for axisymmetric flows through porous media

2015 ◽  
Vol 26 (04) ◽  
pp. 1550036 ◽  
Author(s):  
Fumei Rong ◽  
Baochang Shi
Keyword(s):  
Porous Media ◽  
Distribution Function ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Lattice Boltzmann Model ◽  
Large Pressure ◽  
Flows Through Porous Media ◽  
Simple Processing ◽  
Boltzmann Model ◽  
Good Agreement

In this paper, an axisymmetric LBE model for incompressible flows through porous media is proposed. In this model, the influence of density change caused by large pressure difference can be overcome by replacing density distribution function with pressure distribution function. A more simple processing format for external force is introduced so as to make the involved method in this paper more perfect. The coupling between flow velocity and pressure also can be significantly reduced when calculating the macroscopic quantities. Good agreement between the analytical solution and numerical results is also obtained based on this model and it also can provide guidance for other problem with such complicated force forms.

LATTICE BOLTZMANN MODEL FOR SIMULATING VISCOUS COMPRESSIBLE FLOWS

2010 ◽  
Vol 21 (03) ◽  
pp. 383-407 ◽  
Author(s):  
Y. WANG ◽  
Y. L. HE ◽  
Q. LI ◽  
G. H. TANG ◽  
W. Q. TAO
Keyword(s):  
Distribution Function ◽  
Kernel Function ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Present Model ◽  
Mach Reflection ◽  
Lattice Boltzmann Model ◽  
Polynomial Kernel ◽  
Viscous Compressible Flows ◽  
Boltzmann Model

A lattice Boltzmann model is developed for viscous compressible flows with flexible specific-heat ratio and Prandtl number. Unlike the Maxwellian distribution function or circle function used in the existing lattice Boltzmann models, a polynomial kernel function in the phase space is introduced to recover the Navier–Stokes–Fourier equations. A discrete equilibrium density distribution function and a discrete equilibrium total energy distribution function are obtained from the discretization of the polynomial kernel function with Lagrangian interpolation. The equilibrium distribution functions are then coupled via the equation of state. In this framework, a model for viscous compressible flows is proposed. Several numerical tests from subsonic to supersonic flows, including the Sod shock tube, the double Mach reflection and the thermal Couette flow, are simulated to validate the present model. In particular, the discrete Boltzmann equation with the Bhatnagar–Gross–Krook approximation is solved by the finite-difference method. Numerical results agree well with the exact or analytic solutions. The present model has potential application in the study of complex fluid systems such as thermal compressible flows.

scholarly journals Rectangular lattice Boltzmann model for nonlinear convection–diffusion equations

2011 ◽  
Vol 369 (1944) ◽  
pp. 2311-2319 ◽  
Author(s):  
Jianhua Lu ◽  
Zhenhua Chai ◽  
Baochang Shi ◽  
Zhaoli Guo ◽  
Guoxiang Hou
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Lattice Boltzmann Model ◽  
Diffusion Equations ◽  
Equilibrium Distribution Function ◽  
Rectangular Lattice ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Boltzmann Model

In this paper, a rectangular lattice Boltzmann model is proposed for nonlinear convection–diffusion equations (NCDEs). The model can be used to solve NCDEs with very general form by using a real/complex-valued quadric equilibrium distribution function and relaxation time. Detailed simulations on several examples are performed to validate the model. The numerical results show good agreement with the analytical solutions, and the numerical accuracy is much better than that of the models with a linear equilibrium distribution function.

scholarly journals LATTICE BOLTZMANN APPROACH TO HIGH-SPEED COMPRESSIBLE FLOWS

2007 ◽  
Vol 18 (11) ◽  
pp. 1747-1764 ◽  
Author(s):  
X. F. PAN ◽  
AIGUO XU ◽  
GUANGCAI ZHANG ◽  
SONG JIANG
Keyword(s):  
Lattice Boltzmann ◽  
High Speed ◽  
Compressible Flows ◽  
Velocity Model ◽  
Lattice Boltzmann Model ◽  
Model Parameters ◽  
Von Neumann ◽  
Dissipation Term ◽  
Fluid Systems ◽  
Boltzmann Model

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara15 and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios (1000:1) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

COUPLED DOUBLE-DISTRIBUTION-FUNCTION LATTICE BOLTZMANN MODEL WITH AN ADJUSTABLE BULK VISCOSITY

2008 ◽  
Vol 19 (12) ◽  
pp. 1919-1938 ◽  
Author(s):  
Q. LI ◽  
Y. L. HE ◽  
Y. J. GAO
Keyword(s):  
Distribution Function ◽  
Prandtl Number ◽  
Specific Heat ◽  
Bulk Viscosity ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Specific Heat Ratio ◽  
Boltzmann Model ◽  
Correction Terms

A coupled double-distribution-function (DDF) lattice Boltzmann method was recently developed for the compressible Navier–Stokes equations. In this method, the specific-heat ratio and the Prandtl number can be easily adjusted. However, the ratio between the bulk and shear viscosities is fixed at a value related to the specific-heat ratio. In order to obtain a bulk viscosity satisfying the Stokes' hypothesis or an adjustable bulk viscosity in the recovered momentum and energy equations, correction terms, which are proportional to the divergence of macroscopic velocity, are incorporated into the microscopic evolution equations. The constraints imposed on these correction terms can be derived from the Chapman–Enskog analysis. With these constraints, the forms of the correction terms can be determined, and then a coupled DDF lattice Boltzmann model with adjustable specific-heat ratio, Prandtl number, and bulk viscosity can be obtained. Numerical simulations are performed for the attenuation of sound waves. The numerical results are found to be in good agreement with the theoretical solutions.

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